In this paper, a 2D numerical modeling of sound wave propagation in a shallow water medium that acts as a waveguide, are presented. This modeling is based on the method of characteristic which is not constrained by the Courant–Friedrichs–Lewy (CFL) condition. Using this method, the Euler time-dependent equations have been solved under adiabatic conditions inside of a shallow water waveguide which is consists of one homogeneous environment of water over a rigid bed. In this work, the stability and precision of the method of characteristics (MOC) technique for sound wave propagation in a waveguide were illustrated when it was applied with the semi-Lagrange method. The results show a significant advantage of the method of characteristics over the finite difference time domain (FDTD) method.